Densitometers of the vibrator type which are immersed in a liquid or other substance whose density is to be measured are known in the art. Such instruments have been developed for various uses and are exemplified by the liquid densitometer disclosed in U.S. Pat. No. 4,129,031 to Stephen W. Tehon et al, which is assigned to the assignee of the present application. As shown in the patent, a pair of cylinders, positioned on a common axis, is attached to opposite ends of a compliant torsion spring supported at its nodal point intermediate the spring ends. Each cylinder has structurally defined spaces through which the ambient liquid may pass when the spring mass system is immersed therein.
First and second pairs of transducers are positioned near the opposite ends of the spring. Each transducer is capable of converting between different forms of energy or energy domains, i.e. from stored potential energy produced by the physical distorsion of the transducer, to electrical energy and vice versa. The application of a first electrical signal to the first transducer pair produces distortion in each of these transducers, which is transmitted through the spring to the second transducer pair. The second transducer pair responds by generating a second signal whose amplitude and polarity depends on the magnitude and direction of the distortion of these transducers. The second signal is amplified and applied to the first transducer pair so as to set up a regenerative loop which oscillates at the natural resonant frequency of the spring mass system. Since the liquid contained in the cylinder spaces of the immersed apparatus is part of the overall spring mass system, the frequency of oscillation is a measure of the density of the liquid in the spaces.
While the system disclosed in the referenced patent represents a substantial advance in the densitometer art over systems theretofore available for carrying out such measurements, it nevertheless includes areas susceptible of further improvement. Thus, the size of the transducers is determined by the dimensions of the torsion spring, which is seen to be a compliant bar. The size of the bar is determined by the desired parameters of the spring mass system and its cross-sectional dimensions must generally be kept small. The transducers are therefore likewise limited in size and hence their impedance is low. This results in a low signal-to-noise ratio which is improved somewhat by using a pair of transducers at each spring end. The manner in which the transducers are positioned on the bar spring subjects them to only a portion of the torsional load to which the bar spring itself is subjected. Thus, the position of the transducers in the instrument shown in the referenced patent is another factor which contributes to keeping the maximum obtainable output signal small.
In a practical example of a densitometer of the type shown in the patent, the impedance of a single transducer was on the order of 50 pf. The obtainable output signal is correspondingly low, e.g. around 50 mv when the transducer is driven at 20 volts peak-to-peak. Thus, under high noise condition, for example when the densitometer measures the density of the fuel in the wing fuel tank of an aircraft, the low signal-to-noise ratio may affect closed loop performance.
Another such area in prior art densitometers of the type under discussion here arises from the fact that the transducers contribute to the spring effect by being directly positioned on the spring. Since the transducer modulus of elasticity is sensitive to temperature changes, the spring modulus of elasticity will then also vary with temperature. If the temperature range to which the instrument is subjected varies widely, e.g. from -50.degree. C. to +60.degree. C. when the densitometer is used in aircraft in the manner discussed above, the accuracy of the instrument over the total temperature range may be affected. Experience with some prior art vibrator type densitometers has shown that the instrument error for the temperature range given above may be on the order of +4%. For critical measurements it is desirable to reduce this margin of error.
A further factor which must be kept in mind with respect to such instruments is the inherent brittleness of the transducer material. The transducers typically consist of piezoelectric ceramic material, such as lead zirconate titanate or the like, and they are preferably manufactured in flat shapes for reasons of cost as well as structural stability. Where a more intricate shape is required, such as is the case in instruments of the type shown in the patent, the fabrication costs rise correspondingly.